I'm trying to determine how to load balance TCP traffic. I understand how HTTP load balancing works because it is a simple Request / Response architecture. However, I'm unsure of how you load balance TCP traffic when your servers are trying to write data to other clients. I've attached an image of the work flow for a simple TCP chat server where we want to balance traffic across N application servers. Are there any load balancers out there that can do what I'm trying to do, or do I need to research a different topic? Thanks.
Firstly, your diagram assumes that the load balancer is acting as a (TCP) proxy, which is not always the case. Often Direct Routing (or Direct Server Return) is used, or Destination NAT is performed. In both cases the connection between backend server and the client is direct. So in this case it is essentially the TCP handshake that is distributed amongst backend servers. See the following for more info:
Obviously TCP proxies do exist (HAProxy being one), in which case the proxy manages both sides of the connecton, so your app would need to be able to identify the client by the incoming IP/Port (which would happen to be from the proxy rather than the client). The proxy will handle getting the messages back to the client.
Either way, it comes down to application design as I would imagine the tricky bit is having a common session store (a database of some kind, or key=>value store such as Redis), so that when your app server says "I need to send a message to Frank" it can determine which backend server Frank is connected to (from DB), and signal that server to send it the message. You reduce the problem of connections (from the same client) moving around different backend servers by having persistent connections (all load balancers can do this), or by using something intrinsically persistent like a websocket.
This is probably a vast oversimplification as I have no experience with chat software. Obviously DB servers themselves can be distributed amongst several machines, for fault-tolerance and load balancing.